An inelastic ball is dropped from a height of $100\, m$. Due to the impact,$20\%$ of its energy is lost. To what height will the ball rise?

Two identical balls $A$ and $B$ of equal mass $m$ are lying on a smooth surface as shown in the figure. If ball $A$ hits ball $B$ at rest with a velocity $16 \,ms^{-1}$,then the coefficient of restitution $e$ between $A$ and $B$ so that $B$ just reaches the highest point of the smooth inclined plane of height $5 \,m$ is $\left(g=10 \,ms^{-2}\right)$

$A$ rubber ball is dropped from a height of $5 \ m$ on a planet where the acceleration due to gravity is unknown. After bouncing,the ball reaches a height of $1.8 \ m$. What fraction of its velocity does the ball lose upon impact?

$A$ bullet of mass $0.01\, kg$ travelling at a speed of $500\, m/s$ strikes and passes horizontally through a block of mass $2\, kg$ which is suspended by a string of length $5\, m$. The centre of gravity of the block is found to rise a vertical distance of $0.1\, m$. What is the speed of the bullet after it emerges from the block? (The time of passing of the bullet is negligible,$g = 9.8\, m/s^2$)

$A$ body falls freely onto a hard horizontal surface. If the coefficient of restitution between the surface and the body is $e = 0.8$,then the ratio of the maximum height to which the body rises after the second impact to the initial height of the body is:

Ball $1$ collides with another identical ball at rest. For what value of coefficient of restitution $e,$ the velocity of the second ball becomes two times that of the first ball after the collision?